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2-56. The winner of the Cash-4-Ever Lottery receives $1000 per week in perpetuity. For this question, assume an Annual Percentage Rate (APR) of 2%. (a) In three sentences or less, explain how this company can pay $1000 per week forever using only a finite initial principal. (b) Derive the formula for the present value of the kth payment, where k ≥ 1 is a natural number. Note: Your answer should depend on k. (c) Write a formula for the present value of the Cash-4-Ever prize.

2-56. The winner of the Cash-4-Ever Lottery receives $1000 per week in perpetuity. For this question, assume an Annual Percentage Rate (APR) of 2%. (a) In three sentences or less, explain how this company can pay $1000 per week forever using only a finite initial principal. (b) Derive the formula for the present value of the kth payment, where k ≥ 1 is a natural number. Note: Your answer should depend on k. (c) Write a formula for the present value of the Cash-4-Ever prize.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2-56. The winner of the Cash-4-Ever Lottery receives $1000 per week in perpetuity. For this question, assume an Annual Percentage Rate (APR) of 2%. (a) In three sentences or less, explain how this company can pay $1000 per week forever using only a finite initial principal. (b) Derive the formula for the present value of the kth payment, where k ≥ 1 is a natural number. Note: Your answer should depend on k. (c) Write a formula for the present value of the Cash-4-Ever prize. (d) Let PV(r) be the present value of the Cash-4-Ever Lottery prize at an APR of r%. Suppose r₁ and r2 are positive numbers with r₁ > r2. Is PV(r₁) greater than PV(r₂)? Explain your reasoning in three sentences or less. 62
Transcribed Image Text:2-56. The winner of the Cash-4-Ever Lottery receives $1000 per week in perpetuity. For this question, assume an Annual Percentage Rate (APR) of 2%. (a) In three sentences or less, explain how this company can pay $1000 per week forever using only a finite initial principal. (b) Derive the formula for the present value of the kth payment, where k ≥ 1 is a natural number. Note: Your answer should depend on k. (c) Write a formula for the present value of the Cash-4-Ever prize. (d) Let PV(r) be the present value of the Cash-4-Ever Lottery prize at an APR of r%. Suppose r₁ and r2 are positive numbers with r₁ > r2. Is PV(r₁) greater than PV(r₂)? Explain your reasoning in three sentences or less. 62
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